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Randomized methods for rank-deficient linear systems



Josef Sifuentes, Zydrunas Gimbutas, Leslie Greengard


We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without additional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix corresponding to a known eigenvalue. The method is based on elementary linear algebra combined with the observation that if the matrix is rank-k deficient, then a random rank k perturbation yields a nonsingular matrix with probability 1.
Electronic Transactions on Numerical Analysis


eigenvectors, integral equations, nullspace, null vectors, randomized algorithms, rank-deficient systems.


Sifuentes, J. , Gimbutas, Z. and Greengard, L. (2015), Randomized methods for rank-deficient linear systems, Electronic Transactions on Numerical Analysis, [online], (Accessed July 18, 2024)


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Created February 12, 2015, Updated October 12, 2021